Juvederm takes 2 weeks to fully settle and for swelling and bruising to subside. Swelling is very normal and could be worse 24-48 hours after the treatment. I would recommend booking a follow up to discuss your concerns.
Swelling is very common after having a filler injected to the lips, I suggest you wait about 2 weeks for the swelling to settle before seeing your final result
Yes it is possible to have lots of swelling, even asymmetric or uneven, usually within the first week after your filler treatment. I would recommend you be patient, take a day or two off from your usual activity, consider taking an oral Arnica supplement (available it health food and vitamin stores) and sleep propped up with extra pillows. It should get gradually better in the next week, and if not you should send a photo to your doctor to discuss. Some physicians will prescribe a small, short course of oral prednisone to people who know they get very swollen after filler injection to their lips, so something to consider for future injections.